Earthquake rescuers in eastern Turkey have pulled a two-week-old girl from the wreckage of an apartment building, freeing her from the arms of her mother, who was still trapped.

The baby, named as Azra Karaduman, was freed from the rubble in the town of Ercis, which was badly hit by the quake. Her mother, Semiha, had been clasping her daughter to her chest.

Television footage showed orange-clad rescuers clapping as the naked infant was carried from the rubble. She was wrapped in a blanket and passed to doctors.

Several hours later the mother, who had been pinned down next to a sofa, was freed, and the child's grandmother was also believed to be alive. Azra's father was thought to be inside the building and it was not known if he had survived.

"I am so excited. What can I say? Let God help them," Azra's other grandmother, Sevim Yigit, said as the infant was rescued.

Two days after the 7.2-magnitude earthquake, however, such success stories are growing rare. A total of 366 people are now known to have died in Van province, near the Iranian border, according to Turkey's disaster and emergency administration. More than 2,200 buildings were destroyed, many of them in the worst-affected zone near Ercis.

Van, the much bigger provincial capital about 60 miles to the south, was also affected by the earthquake, but most of the remaining rescue efforts are concentrated in Ercis.

Another point of media focus in the town has been nine-year-old Oguz Isler, who was pulled on Sunday from another toppled apartment building, where his aunt had lived. Since then he has been outside the wrecked building awaiting news of his parents and other relatives who remain buried inside.

"They should send more people," he said, being comforted by an aunt. The boy had been trapped with his sister and a cousin on a third-floor stairwell as they tried to escape when the quake hit. A steel door fell over him.

He said: "I fell on the ground face down. When I tried to move my head, it hit the door. I tried to get out and was able to open a gap with my fists in the wall but could not move my body further.

"The wall crumbled quickly when I hit it. We started shouting, 'help! we're here'. They found us a few hours later, they took me out about eight-and-a-half hours later." The sister and cousin were also pulled out alive.

Initially there was criticism about the speed of the emergency response, but it now appears to be operating well. The country is used to earthquakes and revamped its response following a severe quake in the north-west in 1999 which killed more than 17,000 people.

Another part of the operation is the provision of emergency shelter to tens of thousands of people whose homes have been destroyed or rendered unsafe amid the regular aftershocks.

"It is a very urgent situation," said Hakki Erskoy, a disaster manager for the Turkish Red Crescent, adding that his organisation was dealing with 40,000 homeless people. "Right now, we are facing a race against time to provide shelter for people."

The organisation has set up tented relief camps in two stadiums in Ercis, and distributed tents to those who prefer to remain near their homes. It was also handing out supplies such as blankets, sleeping bags and heaters.

Some significant relief efforts were being organised via social media such as Twitter and Facebook.

Erhan Çelik, a journalist for Turkey's Kanal 7 TV station, passed to his 22,000 Twitter followers an appeal for people to offer accommodation to those made homeless. Within a few hours, he said, he had received 17,000 emails in response.